Solve for $z$, $ -\dfrac{9}{3z - 9} = -\dfrac{8}{z - 3} - \dfrac{5z + 3}{z - 3} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3z - 9$ $z - 3$ and $z - 3$ The common denominator is $3z - 9$ The denominator of the first term is already $3z - 9$ , so we don't need to change it. To get $3z - 9$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{8}{z - 3} \times \dfrac{3}{3} = -\dfrac{24}{3z - 9} $ To get $3z - 9$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{5z + 3}{z - 3} \times \dfrac{3}{3} = -\dfrac{15z + 9}{3z - 9} $ This give us: $ -\dfrac{9}{3z - 9} = -\dfrac{24}{3z - 9} - \dfrac{15z + 9}{3z - 9} $ If we multiply both sides of the equation by $3z - 9$ , we get: $ -9 = -24 - 15z - 9$ $ -9 = -15z - 33$ $ 24 = -15z $ $ z = -\dfrac{8}{5}$